One quarter of the time till now from midnight and half of the time remaining…
2024
One quarter of the time till now from midnight and half of the time remaining from now up to midnight adds to the present time. What is the present time?
- A.
10:00
- B.
9:36
- C.
10:25
- D.
9:15
Attempted by 499 students.
Show answer & explanation
Correct answer: B
Answer: 9:36
Let x be the present time in hours after midnight.
One quarter of the time since midnight is x/4. Half of the remaining time until midnight is (24 - x)/2. According to the problem these add up to the present time, so:
x/4 + (24 - x)/2 = x
Multiply both sides by 4 to clear denominators: x + 2(24 - x) = 4x
Expand and simplify: x + 48 - 2x = 4x ⇒ 48 - x = 4x
Solve for x: 48 = 5x ⇒ x = 48/5 = 9.6 hours
Convert 0.6 hours to minutes: 0.6 × 60 = 36 minutes, so x = 9 hours 36 minutes.
Therefore the present time is 9:36.